This thesis addresses the need for an optimization method which can simultaneously optimize and balance an aerothermodynamic cycle. The method developed is be able to control cycle design variables at all operating conditions to meet the performance requirements while controlling any additional variables which may be used to optimize the cycle and maintaining all operating limits and engine constraints. The additional variables represent degrees of freedom above what is needed for conservation of mass and energy in the engine system. The motivation for such a method is derived from variable cycle engines, however it is general enough to use with most engine architectures. The method is similar to many optimization algorithms but differs in its implementation to an aircraft engine by combining the cycle balance and optimization using a Newton-Raphson cycle solver to efficiently find cycle designs for a wide range of engine architectures with extra degrees of freedom not needed to balance the cycle. Combination of the optimization with the cycle solver greatly speeds up the design and optimization process. A detailed process description for implementation of the method is provided as well as a proof of concept using several analytical test functions. Finally, the method is demonstrated on a separate flow turbofan model. Limitations and applications of the method are further explored including application to a multi-design point methodology.